Yet Another Approach to Poly-Bergman Spaces

Nikolai Vasilevsk ()
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Nikolai Vasilevsk: CINVESTAV, Department of Mathematics

A chapter in Multivariable Operator Theory, 2023, pp 861-874 from Springer

Abstract: Abstract We present an alternative characterization of the poly-Bergman and true-poly-Bergman function spaces on the unit disk $${\mathbb {D}}$$ D , based on the pure isometry acting on the standard $$L_2$$ L 2 -space over $${\mathbb {D}}$$ D and the representation of this isometry in terms of differential operators. As an application, we give the representation of the Landau magnetic Hamiltonian in its action in $$L_2$$ L 2 -space over $${\mathbb {D}}$$ D . The true-poly-Bergman spaces appear there as the corresponding eigenspaces.

Keywords: Poly-Bergman; True-poly-Bergman; Pure isomerty; Landau magnetic Hamiltonian; Primary 30D60; Secondary 30G30; 30H20 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-50535-5_31

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DOI: 10.1007/978-3-031-50535-5_31

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